Stochastic discount factor (SDF)
Quantitative Finance glossary · Stochastic Calculus & Continuous Time Finance
Definition
The random variable m such that today's price of any asset equals E[m × future payoff]; encapsulates time preference and risk aversion.
Stochastic discount factor (SDF) in plain English
Imagine you could ask, "What is a future dollar worth to me today?" — but the answer changes depending on *when* and in *which* scenario you'd actually receive it. The stochastic discount factor m is that personalized, scenario-by-scenario weight: to price any investment, you multiply each possible future payoff by m and average, giving price = E[m × payoff]. It's high in the bad-times scenarios you dread most (a payoff there is precious) and low when you're already doing fine, which is exactly how it bakes in both impatience (you'd rather have money now) and fear of risk. This one gadget is the backbone of asset-pricing theory because *every* asset — stocks, bonds, options — obeys that same pricing rule.
Also called: SDF
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